Fuzzy set theory classifies objects by how much they belong to sets, not by whether they belong. A fuzzy set is defined by a membership function, which maps points in a feature space to a level of membership in the set. Such classification is useful when a set's boundaries are difficult to define, as is the case for boundaries between sub-species, activities, emotions, and to the point, regions in an image. Of particular interest is the classification of regions of an image into one of two sets: regions that are likely to contain objects of interest and those that are not.
Context clues, prior knowledge, automatic filters, third party observations, or other information may indicate that objects are likely to exist at certain points or regions in an image. Several sources of uncertainty, such as measurement errors, object movement, conflicting information, unreliable sources, and vague correlation with context clues reduce confidence in the precise locations given by the various information sources. Instead of classifying these precise locations as “object likely” or “object unlikely”, it may be more accurate to define “object likely” as a fuzzy set. Regions near where information predicts objects of interest would have high membership. Surrounding regions would have decreasing membership, depending on the distance over which the predictive information is likely to misjudge an object's location. Regions with no nearby indications would have no membership.